Superconductor with two singularities inherent in high-T-c materials,
low carrier density and overlapping of the energy bands on the Fermi s
urface, is considered. Provided T=0, the order parameter Delta(n) and
chemical potential mu are determined in the mean-field approximation f
or the state with Bose condensation of the localized pairs (mu<0). The
equation for the energy of the bound state epsilon(b) is also obtaine
d and the relationship epsilon(b)=2 mu is established. The method of f
unctional integration concerning the two-band model is developed. On t
he basis of this method, the crossover between the Fermi picture and t
he Bose one of the elementary excitations is demonstrated for the syst
em in the presence of the two-particle bound state. The expression for
the temperature of Bose condensation T-k is Obtained and the contribu
tion of the residual interaction between bosons for the systems with a
rbitrary dimension is determined.